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knowl/xref/example-binomial-variance.html
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<span class="type">Example</span><span class="space heading-divison-mark heading-divison-mark__space"> </span><span class="codenumber">3.2.7</span><span class="period heading-divison-mark heading-divison-mark__period">.</span>
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<div class="para">Recall the setup from <a href="sec-Expected-Value.html#example-binomial-EV" class="xref" data-knowl="./knowl/xref/example-binomial-EV.html" data-reveal-label="Reveal" data-close-label="Close" title="Example 3.1.11">Example 3.1.11</a>: a binomial random variable <span class="process-math">\(S\)</span> is the sum <span class="process-math">\(H_1 + H_2 + \dotsb + H_n\)</span> of <span class="process-math">\(n\)</span> indicator random variables, each with parameter <span class="process-math">\(p\text{.}\)</span> The results of different coin flips are independent from each other, so the random variables <span class="process-math">\(H_1, \dotsc, H_n\)</span> are independent from each other. From <a href="sec-Variance.html#example-indicator-variance" class="xref" data-knowl="./knowl/xref/example-indicator-variance.html" data-reveal-label="Reveal" data-close-label="Close" title="Example 3.2.6">Example 3.2.6</a>, we know that <span class="process-math">\(\Var(H_i) = p(1-p)\)</span> for each <span class="process-math">\(i\text{.}\)</span> Therefore:</div>
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<div class="para">Remember this formula! We’ll make frequent use of it.</div>
<div class="autopermalink" data-description="Paragraph"><a href="#example-binomial-variance-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
<div class="autopermalink" aria-hidden="true" data-description="Paragraph"><a tabindex="-1" href="#example-binomial-variance-1-1" title="Copy heading and permalink for Paragraph" aria-label="Copy heading and permalink for Paragraph">🔗</a></div>
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<div class="autopermalink" data-description="Example 3.2.7"><a href="#example-binomial-variance" title="Copy heading and permalink for Example 3.2.7" aria-label="Copy heading and permalink for Example 3.2.7">🔗</a></div></article><span class="incontext"><a class="internal" href="sec-Variance.html#example-binomial-variance">in-context</a></span>
<div class="autopermalink" aria-hidden="true" data-description="Example 3.2.7"><a tabindex="-1" href="#example-binomial-variance" title="Copy heading and permalink for Example 3.2.7" aria-label="Copy heading and permalink for Example 3.2.7">🔗</a></div>
</article><span class="incontext"><a class="internal" href="sec-Variance.html#example-binomial-variance">In Context</a></span>
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